I'm building this post expanding on Danny Beckett's information, give him credit :-)
Since 1919, aircraft registration is based on international prefixes allocated by ITU to radiotelegraphic stations rather than on a specific system. N prefix was allocated to US by ITU in 1919, along with KDA-KZZ and W. The choice for this system for aviation matters is materialized in the Chicago Convention since 1944, and previously in the Paris Convention it extended.
The question boils down to: Why did ITU allocate N and W (plus KDA-KZZ) to the US? instead of U, US or USA? The answer is likely US was not so involved in these matters at the beginning and choices were limited when the interest came:
CINA (which would become ICAO in 1947) and ITU, both at the origin of the prefix system, are also two of the many international peaceful initiatives by European governments to prevent recurrence of conflicts in the region.
ITU membership was reserved to States. Telegraph in the US was considered a matter of private companies, so US Government participation to ITU was not significant in the early years.
US will send an observer to ITU in 1875, 10 years after its creation, and US did agree in 1903 in Berlin that radiotelegraphy between ships and shore would be free to competition (read: Marconi stations would answer non-Marconi stations), but refused to ratify ITU radio regulations (RR) until 1949.
I guess founding members of ITU helped themselves with prefixes, and when the others came they had indeed fewer choices. Whole blocks (single letter prefix) have been allocated to actual or expecting-to-be empires: Germany (A, D), GB (B, G, M, and V for the overseas colonies), France (F), Italia (I), Japan (J), US (N, W), Russia (R).
In the end what was named the "call letters" had to be renamed the "call signs" with the addition of figures, like "2" for Guernsey or "9K" for Kuwait.
Historical milestones in international aviation vs international communication
- 1865: International Telegraph Union (ITU) created in Europe to handle telegraph matters.
- 1875: Saint Petersburg Telegraphic Convention.
- 1906: ITU Berlin Radiotelegraphic Convention. First convention about radiotelegraph.
- 1912: ITU London Radiotelegraphic Convention
- 1913: The International Bureau of the Telegraph Union in Berne releases a list of prefixes for radiocommunication. N and other blocks allocated to US. N has no specific meaning, it just happened to be available.
- 1913: US Department of Commerce makes the International Bureau list applicable in the US, in particular to ships and coastal stations.
- 1913: First passenger-carrying airline
- 1919: Paris Convention on ATC, prepared by CINA, deals with how allies, defeated, and other countries aircraft can be regulated, e.g. can they fly over another country? Part of this is the adoption of the national radio prefixes for aircraft registration and marking too. US did not ratify the convention.
- 1927: Washington Radiotelegraphic Convention, the aircraft marking system based on ITU proposal is agreed (is today Annex 7 of the Chicago Convention).
- 1929: Warsaw Convention sets aviation-related liability laws prepared by Paris-based CITEJA, Comité International Technique des Experts Juridiques Aériens.
- 1932: ITU is renamed International Telecommunication Union (Madrid Convention)
- 1944: Chicago Convention extends Paris Convention and creates PICAO, a temporary organization to replace CINA
- 1947: ITU is now part of UN
- 1947: PICAO becomes ICAO, ICAO is part of UN.
Agreement on radiotelegraph practices and station callsigns
At the beginning of the 20th century, radiotelegraphy ("wireless") was a new technology and communications with ships were handled using several variants of Morse code, Q-Code and protocols, by commercial operators like Marconi, according to their own practices. Even uniqueness of radio station identifiers among all involved stations was not guaranteed.
Such a technology used worldwide required some international agreements on important matters like frequencies, techniques, codes, station identifiers, etc. These agreements were obtained through formal radiotelegraphic conventions, in particular:
These conventions established standards to be implemented by involved stations, of which a standard use of station identifiers (the "call letters").
Agreement on country prefixes for callsigns
Station identifiers had still to be delivered by different States, an agreement had to be found to ensure they would be unique. In April 1913 the International Bureau of the Telegraph Union released a list of national prefixes for station identifier allocation by States. This list was made official in the US by the Department of Commerce, in a document titled "Radio Call Letters", in May 1913:
The Service Regulations of the Berlin and London Radiotelegraphic Conventions provide that the call letters of stations in the
international system must each be formed of a group of three letters
which shall be distinguishable from one another.
The London International Radiotelegraphic Conference made a partial allotment of call letters among nations which signed the convention
and the International Bureau at Berne, with the consent of such
nations, has modified and added to this assignment of call letters by
circular of April 23, 1913.
The distribution of call letters among nations thus authorized is printed below for the guidance of operators of all stations, ship and
shore, of the United States.
Followed a list of international prefixes:
Q was reserved to prevent confusion with Q-Code sequences. The conventions also standardized this code, reserving QAA-QNZ to aviation and QOA–QQZ to marine.
Including KDA-KZZ, N, W for the US. N and W were possibly selected because they were the unassigned whole blocks at the time, while U, a natural choice, was already shared between France/Austria/Hungary/Bosnia-Herzegovina. Just a guess.
US DoC then spit this allotment: N for Government stations, W for stations of the Pacific (and some for the US Army), and KDA-KZZ for stations of the Atlantic.
Commission Internationale de Navigation Aérienne
The Commission Internationale de Navigation Aérienne (CINA) has been the precursor of ICAO. Its role was to help build international air navigation services.
To handle aircraft, ATC needed to identify them, and aircraft had to be registered at the State level, so that they could be linked to some legal system. CINA proposed to use a process similar to the one for radio stations, and to reuse the same ITU prefixes, with some minor adjustments (like adding a hyphen after the prefix) but also some changes, e.g. Germany was removed from the countries with a prefix:
This proposition was adopted at Paris Convention in 1919. Paris Convention would later be extended by Chicago convention, and CINA replaced by ICAO, an organization of the UN. The prefixes would be updated in 1929 to the ones used today.
International Telecommunication Union (ITU) still maintains the list of prefix blocks in Appendix 42 of the Radio Regulations, and ITU is a full member of ICAO (without vote right).
More in Annex 7 – Aircraft Nationality and Registration Marks (commented here)